Math / Algebra

Question\text{Calculate the heat (in kJ) associated with the cooling of } 392 \, \text{g of mercury from } 74.5^{\circ} \text{C to } 12.0^{\circ} \text{C}. \text{ Be sure your answer has the correct number of significant digits.} \\ \text{Note: Reference the Phase change properties of pure substances table for additional information.} \\ \text{Specific heat capacity of mercury: } 0.139 \, \text{J/gK} \\ \Box \, \text{kJ} \, \Box \times 10 \\

Studdy Solution

STEP 1

1. The mass of mercury is 392 grams.
2. The initial temperature of mercury is $74.5^{\circ} \text{C}$ .
3. The final temperature of mercury is $12.0^{\circ} \text{C}$ .
4. The specific heat capacity of mercury is $0.139 \, \text{J/gK}$ .
5. We need to calculate the heat in kilojoules (kJ).
6. The answer should have the correct number of significant digits.

STEP 2

1. Calculate the change in temperature.
2. Use the formula for heat transfer to calculate the heat in joules.
3. Convert the heat from joules to kilojoules.
4. Ensure the answer has the correct number of significant digits.

STEP 3

Calculate the change in temperature ( $\Delta T$ ).
$\Delta T = T_{\text{final}} - T_{\text{initial}} = 12.0^{\circ} \text{C} - 74.5^{\circ} \text{C} = -62.5^{\circ} \text{C}$

STEP 4

Use the formula for heat transfer: $q = m \cdot c \cdot \Delta T$ , where $q$ is the heat, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature.
$q = 392 \, \text{g} \times 0.139 \, \text{J/gK} \times (-62.5 \, \text{K})$
$q = 392 \times 0.139 \times (-62.5) \, \text{J}$
$q = -3405.05 \, \text{J}$

STEP 5

Convert the heat from joules to kilojoules.
$q = -3405.05 \, \text{J} \times \frac{1 \, \text{kJ}}{1000 \, \text{J}} = -3.40505 \, \text{kJ}$

STEP 6

Ensure the answer has the correct number of significant digits. The least number of significant digits in the given values is 3 (from the mass of mercury, 392 g).
Thus, the heat associated with the cooling of mercury is:
$\boxed{-3.41 \, \text{kJ}}$

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Studdy Solution

STEP 1

STEP 2

1. Calculate the change in temperature.
2. Use the formula for heat transfer to calculate the heat in joules.
3. Convert the heat from joules to kilojoules.
4. Ensure the answer has the correct number of significant digits.

STEP 3

Calculate the change in temperature ( $\Delta T$ ).
$\Delta T = T_{\text{final}} - T_{\text{initial}} = 12.0^{\circ} \text{C} - 74.5^{\circ} \text{C} = -62.5^{\circ} \text{C}$

STEP 4

STEP 5

Convert the heat from joules to kilojoules.
$q = -3405.05 \, \text{J} \times \frac{1 \, \text{kJ}}{1000 \, \text{J}} = -3.40505 \, \text{kJ}$

STEP 6

Ensure the answer has the correct number of significant digits. The least number of significant digits in the given values is 3 (from the mass of mercury, 392 g).
Thus, the heat associated with the cooling of mercury is:
$\boxed{-3.41 \, \text{kJ}}$

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Studdy Solution

STEP 1

STEP 2

1. Calculate the change in temperature.2. Use the formula for heat transfer to calculate the heat in joules.3. Convert the heat from joules to kilojoules.4. Ensure the answer has the correct number of significant digits.

STEP 3

Calculate the change in temperature (ΔT\Delta TΔT).ΔT=Tfinal−Tinitial=12.0∘C−74.5∘C=−62.5∘C\Delta T = T_{\text{final}} - T_{\text{initial}} = 12.0^{\circ} \text{C} - 74.5^{\circ} \text{C} = -62.5^{\circ} \text{C}ΔT=Tfinal​−Tinitial​=12.0∘C−74.5∘C=−62.5∘C

STEP 4

STEP 5

Convert the heat from joules to kilojoules.q=−3405.05 J×1 kJ1000 J=−3.40505 kJq = -3405.05 \, \text{J} \times \frac{1 \, \text{kJ}}{1000 \, \text{J}} = -3.40505 \, \text{kJ}q=−3405.05J×1000J1kJ​=−3.40505kJ

STEP 6

Ensure the answer has the correct number of significant digits. The least number of significant digits in the given values is 3 (from the mass of mercury, 392 g).Thus, the heat associated with the cooling of mercury is:−3.41 kJ\boxed{-3.41 \, \text{kJ}}−3.41kJ​

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1. Calculate the change in temperature.
2. Use the formula for heat transfer to calculate the heat in joules.
3. Convert the heat from joules to kilojoules.
4. Ensure the answer has the correct number of significant digits.

Calculate the change in temperature ( $\Delta T$ ).
$\Delta T = T_{\text{final}} - T_{\text{initial}} = 12.0^{\circ} \text{C} - 74.5^{\circ} \text{C} = -62.5^{\circ} \text{C}$

Convert the heat from joules to kilojoules.
$q = -3405.05 \, \text{J} \times \frac{1 \, \text{kJ}}{1000 \, \text{J}} = -3.40505 \, \text{kJ}$

Ensure the answer has the correct number of significant digits. The least number of significant digits in the given values is 3 (from the mass of mercury, 392 g).
Thus, the heat associated with the cooling of mercury is:
$\boxed{-3.41 \, \text{kJ}}$